Question

select the correct answer.

at the auditions, 40 students tried out for the school show choir, but only 12 will be chosen. how many different ways can the show choir be formed?

a. 479,001,600

b. 847,660,528

c. 2,311,801,440

d. 5,586,853,480

Explanation:

Step1: Identify combination formula

We use combinations since the order of choosing students does not matter. The formula for combinations is:
$$C(n,k)=\frac{n!}{k!(n-k)!}$$
where $n=40$ (total students) and $k=12$ (students to choose).

Step2: Substitute values into formula

$$C(40,12)=\frac{40!}{12!(40-12)!}=\frac{40!}{12!\times28!}$$

Step3: Simplify the expression

Cancel out $28!$ from numerator and denominator:
$$C(40,12)=\frac{40\times39\times38\times\cdots\times29}{12\times11\times10\times\cdots\times1}$$
Calculate the product:
$$C(40,12)=2311801440$$

Answer:

C. 2,311,801,440